Of `f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)(lambda^2-5lambda+3)x+10` is a decreasing function for all `x in R ,` find the permissible values of `lambdadot`

Explanation

To solve the problem, we need to find the permissible values of \( \lambda \) such that the function

\[ f(x) = \frac{2}{\sqrt{3}} \tan^{-1}\left(\frac{2x+1}{\sqrt{3}}\right) - \log(x^2 + x + 1) + (\lambda^2 - 5\lambda + 3)x + 10 \]

is a decreasing function for all \( x \in \mathbb{R} \).

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